Analysis of stress impact on transistor performance

ABSTRACT

Roughly described, a method for approximating stress-induced mobility enhancement in a channel region in an integrated circuit layout, including approximating the stress at each of a plurality of sample points in the channel, converting the stress approximation at each of the sample points to a respective mobility enhancement value, and averaging the mobility enhancement values at all the sample points. The method enables integrated circuit stress analysis that takes into account stresses contributed by multiple stress generation mechanisms, stresses having vector components other than along the length of the channel, and stress contributions (including mitigations) due to the presence of other structures in the neighborhood of the channel region under study, other than the nearest STI interfaces. The method also enables stress analysis of large layout regions and even full-chip layouts, without incurring the computation costs of a full TCAD simulation.

RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 12/510,190, filed 27Jul. 2009, by Victor Moroz and Dipankar Pramanik, entitled “ANALYSIS OFSTRESS IMPACT ON TRANSISTOR PERFORMANCE,” Atty. Docket No. SYNP 0693-6,which application is a divisional of U.S. application Ser. No.11/291,294, filed 1 Dec. 2005, by Victor Moroz and Dipankar Pramanik,entitled “ANALYSIS OF STRESS IMPACT ON TRANSISTOR PERFORMANCE,” Atty.Docket No. SYNP 0693-1, which applications are incorporated herein byreference in their entirety.

FIELD OF THE INVENTION

The invention relates to the modeling of integrated circuit devices, andmore particularly to the modeling of stress impact on transistorperformance.

BACKGROUND AND SUMMARY OF THE INVENTION

It has long been known that semiconductor materials such as silicon andgermanium exhibit the piezoelectric effect (mechanical stress-inducedchanges in electrical resistance). See for example C. S. Smith,“Piezoresistance effect in germanium and silicon”, Phys. Rev., vol. 94,pp. 42-49 (1954), incorporated by reference herein. The piezoelectriceffect has formed the basis for certain kinds of pressure sensors andstrain gauges, but only recently has it received attention in themanufacture of integrated circuits. In integrated circuit fabrication,one of the major sources of mechanical stress is the differentialexpansion and contraction of the different materials used. For example,typical fabrication technologies involve electrically isolating theactive regions of groups of one or more transistor by surrounding themwith shallow trench isolation (STI) regions which are etched into thesilicon and then filled with an insulator, such as an oxide. Duringcooling, oxides tend to shrink less than the surrounding silicon, andtherefore develop a state of compressive stress laterally on the siliconregions of the device. Of significance is the stress exerted by the STIregions on the silicon forming a Metal-Oxide-Semiconductor Field-EffectTransistor (MOSFET) channel, because the piezoelectric impact of suchstress can affect carrier mobility, and therefore current flow throughthe channel (Ion). In general, the higher the electron mobility in thechannel, the faster the transistor switching speed.

The stress exerted on a region of silicon decays rapidly as a functionof distance from the stress-causing interfaces. In the past, therefore,while process technologies could not produce today's extremely narrowchannel widths, the stress-induced impact on performance could beignored because only the edges of the diffusion region (adjacent to theSTI regions) were affected. The channel regions were too far away fromthe STI regions to exhibit any significant effect. As processtechnologies have continued to shrink, however, the piezoelectric effecton transistor performance is no longer negligible.

Technology Computer Aided Design (TCAD) models are frequently used tomodel the behavior of integrated circuit devices at the level ofindividual transistors. Behaviors characterized at this level can be fedback to improve the circuit layout or the fabrication process, or theycan be used to derive circuit level parameters (e.g. SPICE parameters)of the device for subsequent analysis of the circuit at macroscopiclevels. TCAD analysis has long been able to take stress effects intoaccount, but only by performing 3-dimensional finite element analysis ofa single transistor or a small fragment of the chip. The computationtime required to obtain accurate results, however, limited the utilityof this kind of analysis to only small regions of a chip layout thatinclude only several transistors. For example, it has not been practicalto perform a TCAD analysis to obtain reasonably accurate circuit levelparameters for layout regions larger than about a dozen transistors, orabout 2-3 diffusion regions. Even then, huge amounts of CPU time, up toseveral hours per transistor, were required to obtain reasonablyaccurate results. The required computation time makes this approachprohibitively expensive for any large fragments of the chip layout.

Recently, a simplified model was developed for approximating stresseffects on electron and hole mobilities. See R. A. Bianchi et al.,“Accurate Modeling of Trench Isolation Induced Mechanical Stress Effectson MOSFET Electrical Performance,” IEEE IEDM Tech. Digest, pp. 117-120(December 2002), and U.S. Patent Publication No. 2002/0173588 (2003),both incorporated herein by reference. A variation of this model, withsome additional fitting terms and parameters, was incorporated intoRevision 4.3.0 of the Berkeley BSIM standard model. See Xuemei (Jane)Xi, et al., “BSIM4.3.0 Model, Enhancements and Improvements Relative toBSIM4.2.1”, University of California at Berkeley (2003), available athttp: (slash)(slash)www-device.eecs.berkeley.edu/˜bsim3/BSIM4/BSIM430/doc/BSIM430_Enhancement.pdf,incorporated by reference herein. The model is known as the Length ofDiffusion (LOD) model, since its primary parameter is the length of thediffusion region on each side of the channel of a transistor understudy. Roughly, the model analyzes the layout to find the LOD atdifferent segments along the width of the channel, calculates a weightedaverage LOD for the entire channel width, calculates a stress based onthe weighted average LOD, and then converts that stress value to achange in mobility.

There are a number of problems with the LOD model. First, the model islimited to STI-induced stress. It therefore ignores many other potentialsources of stress. For example, some integrated circuit manufacturersform SiGe in the source and drain areas of a p-channel transistorintentionally to induce certain stresses on the channel; this source ofstress is not taken into account in the LOD model, nor are stressesinduced by differential coefficients of expansion of superposing layers.Additionally, several semiconductor manufacturers use strained caplayers covering the transistors on top of the gate stacks. It is typicalto use tensile nitride cap layers for n-channel transistors andcompressive nitride cap layers for p-channel transistors. Some otherpotential stress sources include tensile STI that is beneficial for bothn-channel and p-channel transistors and tensile Si:C (carbon-dopedsilicon) in the source/drain of the n-channel transistors. None of thesestress sources are taken into account by the LOD methodology.

Second, the LOD model fails to take into account stresses that might bepresent transversely to the length of diffusion, across the channelwidth-wise. It has been discovered that compressive stress in thisdirection can affect carrier mobility in the channel in significant andsurprising ways.

Third, more generally than the second deficiency, since the LOD modelconsiders only hydrostatic pressure, which is a sum of all normal (i.e.volume changing rather than rotational) stress components, it fails totake into account differing vector stress components. Different stresscomponents relative to the channel direction are known to affect carriermobility differently.

Fourth, the LOD model fails to take into account the presence of otherstructures in the neighborhood of a region under study, apart from thenearest STI interface. Other structures beyond this interface mightreduce the amount of oxide presumed to be exerting a force, andtherefore might reduce the actual stress in the channel.

Accordingly, it would be extremely desirable to provide a stressanalysis method that approximates the stresses in a region of anintegrated circuit chip, more accurately than does the LOD model, andwithout incurring the computation costs of a 3-dimensional finiteelement analysis. Such a method can enable stress analysis of muchlarger regions of the circuit, including of an entire integrated circuitchip.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with respect to specific embodimentsthereof, and reference will be made to the drawings, in which:

FIG. 1 shows an illustrative layout region with three transistors. Thetop portion of the diagram illustrates a plan view of the layout region,and the bottom portion of the diagram illustrates a cross-section takenat sight-line A-A′.

FIGS. 2, 4 and 5 are flowcharts for an embodiment of methods of theinvention.

FIG. 3 shows the plan view of the layout of FIG. 1, with four samplepoints identified.

FIG. 6 illustrates diffusion regions in a portion of the plan view ofthe layout of FIG. 1.

DETAILED DESCRIPTION

In order to best describe an embodiment of the invention, reference willbe made to an illustrative layout portion as shown in FIG. 1. In FIG. 1,the top portion of the diagram illustrates a plan view of the layoutregion, and the bottom portion of the diagram illustrates across-section taken at sight-line A-A′ as shown in the top portion. Thelayout region of FIG. 1 includes three transistors 110, 112 and 114,plus some other structures 116, 118, 120 and 122. Referring totransistor 114 as an example, it comprises a diffusion region 124 whichis crossed by a gate conductor 126. The portion of the diffusion region124 to the left of the gate 126 is the source diffusion region of thetransistor, and the portion to the right of the gate 126 is the draindiffusion region. The portion of the diffusion region 124 overlappingwith below the gate 126 is the channel 128 of the transistor. As usedherein, the term “region” represents a two-dimensional area in a planview of the layout. Stress “in” a region is considered to be the stressclose to the surface of the region, where current flows. In theembodiments described herein, an approximation is made that the stress“in” a region is equal to the stress “at” the surface of the region. Inanother embodiment, stresses within a volume of the chip can be takeninto account as well, including at depths below the surface.

The description herein will also be assisted if the followingdefinitions are established. As shown in FIG. 1, as used herein, the“longitudinal” direction of a transistor is the direction of currentflow from source to drain when the transistor is turned on. The“transverse” direction is perpendicular to the longitudinal direction,and perpendicular to the direction of current flow. Both thelongitudinal and transverse directions of the transistor are consideredto be “lateral” directions, meaning a direction that is parallel to thesurface. Other “lateral” directions include those (not shown) which areparallel to the surface but intersect both the transverse andlongitudinal directions at angles. The “vertical” direction is normal tothe surface of the channel and therefore perpendicular to all possiblelateral directions. The “length” of a structure in the layout is itslength in the longitudinal direction, and its “width” is its width inthe transverse direction. It can be seen from the layout of transistor114 that the length of its channel 128 is a significantly shorter thanits width, which is typical for the transistors that are used in logiccircuits. Also shown in FIG. 1 are the X, Y, and Z coordinate axes. Inthe layout of FIG. 1, the X direction is the same as the longitudinaldirection, the Y direction is the same as the transverse direction, andthe Z direction is perpendicular to both the longitudinal and transversedirections, representing a depth into the integrated circuit chip.

In the layout of FIG. 1, transistors 110 and 112 share a commondiffusion region 130. In addition, all regions in the plan view of FIG.1 outside the diffusion regions 116, 130, 124, 118, 120 or 122, are STIregions containing oxide. Three of the STI regions can be seen in thecross-sectional view, specifically region 132, disposed betweendiffusion regions 116 and 130; region 134, disposed between diffusionregions 130 and 124; and region 136, disposed between diffusion regions124 and 118. All these STI regions exert compressive stress on thediffusion regions, including within the transistor channels. In theprior art LOD model, only the stresses exerted in the longitudinaldirection are taken into account. The methods described herein, on theother hand, can take into account stresses in the transverse andvertical directions as well.

The methods described herein can also take into account stressmitigating features, whereas the LOD method cannot. For example, the STIregion 134 exerts a particular stress longitudinally toward the channelsof transistors 112 and 110, and that stress is maximum at the interfacebetween the STI region 134 and the diffusion region 130 and decays by apredetermined function of distance toward the channels. The LOD methodassumes that the STI region to the right of the interface has aparticular typical length in that direction, and therefore assumes aparticular maximum stress value at the interface. But another diffusionregion 124 is present in the layout of FIG. 1, only a short distance tothe right of that interface. Thus the length of the STI region mayactually be very short, which would reduce the actual stress on the twochannel regions. Some of the methods described herein avoid thisinaccuracy by taking into account stress mitigating features, such asthe presence of diffusion region 124.

The methods described herein can also take into account the stressescaused by other stress generation mechanisms aside from STI/siliconinterfaces. For example, in an embodiment in which the source and drainregions of the p-channel transistors are formed of silicon-germaniumalloy, but the channel regions are not, stresses are exerted on thechannel regions due to the crystal lattice mismatch at their interfacewith the silicon-germanium alloy regions. These stresses, too, can betaken into account by methods described herein. As used herein, a“stress generation mechanism” is one that arises at an interface betweena pair of different materials. Typically the stress arises due to eitherthermal mismatch or crystal lattice mismatch or built-in stress obtainedas a consequence of specific deposition chemistry. Two stress generationmechanisms are themselves considered herein to be “different” if theydiffer in at least one material of the pair. Two stress generationmechanisms are themselves considered herein to be different also if theyarise from different physical principles, even where the material pairsare the same.

FIG. 2 is an overall flowchart of an embodiment of the invention. Aswith all flowcharts herein, it will be appreciated that many of thesteps can be combined, performed in parallel or performed in a differentsequence without affecting the functions achieved. In some cases are-arrangement of steps will achieve the same results only if certainother changes are made as well, and in other cases a re-arrangement ofsteps will achieve the same results only if certain conditions aresatisfied.

Referring to FIG. 2, in a step 210, the system first starts a loopthrough selected transistors in a layout. Because of the speed andaccuracy with which mobility enhancement values can be determined usingfeatures of the present invention, it is feasible to determine modifiedcarrier mobilities for all transistors on the integrated circuit chip.Alternatively, a user may select only certain important transistors,such as those along one of the critical paths. Embodiments of theinvention enable reasonably accurate analysis of layout regionscollectively containing more than 12 or so transistors, or more than 3diffusion regions, both of which were impractical or impossible withconventional methods. For purposes of illustration, it will be assumedthat the first transistor selected in step 210 is transistor 112 (FIG.1).

In step 212, the system identifies the channel region of the selectedtransistor. The channel region can be identified by the intersection ofthe gate and diffusion layout layers.

In step 214, several sample points are selected in the channel. FIG. 3shows the plan view of the layout of FIG. 1, with four sample points 310identified in the channel region 300 of the transistor 112. In FIG. 1the sample points lie on a line oriented transversely across thechannel, and in the middle of the channel longitudinally, and the samplepoints are spaced uniformly along that line within the channel. Ingeneral, the effort is to estimate the stress distribution throughoutthe channel. Since the channel is typically very short in thelongitudinal direction, it is usually sufficient to choose sample pointsall in a single laterally-oriented line disposed in the center of thechannel longitudinally. But since the channel is typically very widelaterally, relatively speaking, several sample points across the channellaterally are usually required to develop an accurate estimate of thestress distribution throughout the channel. The designer will choose anumber of sample points across the channel that represents an acceptablecompromise between accuracy, which improves with more sample points, andspeed of analysis, which improves with fewer sample points.

In step 216 the stress at each of the sample points 310 is approximated.(As used herein, the term “approximation” includes exactness as aspecial case. Therefore it is possible that in some instances theapproximations developed in step 216 will be exact.) FIG. 4 is aflowchart detail of step 216. In step 408, the routine begins by loopingthrough all the sample points. In step 410, if there is more than onestress generation mechanism to be taken into account, the system beginsa loop through all of the stress generation mechanisms to be taken intoaccount. For example, STI-induced stresses can be taken into account, aswell as silicon-germanium-induced stresses. Other stresses can also betaken into account, such as those induced by a silicide layer that isgrown on top of the source and drain areas and those induced by thestrained cap layers that cover the gate stacks.

In step 412, a search region is determined for the current sample pointand stress generation mechanism. The search region should be largeenough to include layout features outside the diffusion regioncontaining the sample point, but since stress decays with distance, itshould not extend to such a great distance that the stress contributionat the sample point is negligible. In one embodiment, a rectangularregion can be chosen. In another embodiment, a circular region with apredefined radius can be chosen. Typically, the greater the depth intothe wafer at which the current stress generation mechanism contributesto the stress at the surface of the wafer, the larger the search regionshould be. As an example, for STI-induced stress, the search radiusmight be approximately 2 microns and encompass (with current technology)16-20 transistors. The search radius for silicon-germanium-inducedstress would typically be smaller, since the silicon-germaniumsource/drain regions are typically much shallower than STI.

In step 414, the system combines the approximate stress contributions tothe stress at the current sample point, due to the current stressgeneration mechanism, of each stress source in the current searchregion. As used herein, the “combining” of values means evaluating thevalues together in a predetermined mathematical function. In the presentembodiment, an assumption is made that the stress contributions from allsources and all stress generation mechanisms are additive, and so instep 414, the system simply sums the approximate stress contributions.

In one embodiment, the combining of approximate stress contributions caninvolve dividing the search region into a rectangular grid andcalculating the stress caused by each grid rectangle in which there is asource of stress. In a preferred embodiment, however, these stresscontributions are approximated using an edge walking technique such asthat illustrated in the flow chart of FIG. 5.

In the method of FIG. 5, the contribution of each edge in the currentsearch region to the stress at the current sample point due to thecurrent stress generation mechanism, is approximated. In a preferredembodiment, this approximation takes into account stress components inthe X and Y directions independently. The edges that are walked arethose shown in the plan view of FIG. 1, which all lie in either the Xdirection or the Y direction. The edges that are parallel to the X axiswill introduce stress along both lateral directions X and Y. Similarly,the edges that are parallel to the Y axis will introduce stress alongboth lateral directions X and Y. The stress introduced in X direction byan edge that is parallel to the Y axis is identical to the stressintroduced in Y direction by an edge that is parallel to the X axis forthe same stress generation mechanism. This stress component is sometimesreferred to herein as a normal stress component. The stress introducedin X direction by an edge that is parallel to the X axis is, in turn,identical to the stress introduced in Y direction by an edge that isparallel to the Y axis for the same stress generation mechanism. Thisstress component is sometimes referred to herein as a tangential stresscomponent.

In one embodiment, the layout is restricted to edges that are alignedwith the X and Y Cartesian axes in the layout plane. In anotherembodiment, the edges of the layout features can have arbitrary shapes,usually described as polygons with edges that are oriented arbitrarilyin the X-Y layout plane. This can be important whenever there aresignificant optical proximity effects that distort the originalrectangular layout.

The depth of the edges into the wafer is taken into account in thepresent embodiment not by calculating a stress component in the Zdirection, but by appropriate calibration of the stress peak at theedges and the function by which the stress decays with distance. Thiscalibration is discussed below. Stress components in the Z direction dueto edges buried below the surface and not visible in the plan view ofFIG. 1, can also be taken into account independently, but these aregiven only cursory treatment in the present discussion. The reader willunderstand how to extend the methods to include stress contributions inthe Z direction more fully. Several stress sources are known to generatea significant vertical stress component, notably a strained cap layerdeposited over the gate stack. It is known that p-channel transistorsare insensitive to the vertical stress component, whereas n-channeltransistors are very sensitive to the vertical stress component.Calculation of the vertical stress component can be performed in asimilar way to the lateral stress components, with the vertical stressdecaying as a function of distance from transistor to the edges of thestrained cap layers that are located in the XY layout plane.

Referring to FIG. 5, the method begins an outer loop to consider all thefeature edges that appear within the current search region (step 510).The particular edges considered within the loop 510 will depend on thecurrent stress generation mechanism being considered. For example, ifthe current stress generation mechanism is STI-induced stress, then onlythe interfaces between STI regions and diffusion regions are consideredin the loop 414. If the current stress generation mechanism issilicon-germanium-induced stress, then the following two types ofinterfaces are taken into account in the loop 414: the interfacesbetween the silicon-germanium diffusion regions and the silicon channelregions, and the interfaces between the silicon-germanium diffusionregions and the STI. If the current stress generation mechanism underconsideration is the strained cap layer, then the edges of thepolysilicon gates and the edges of the strained cap layers are takeninto account. In many cases the edges are shifted from their originallocation in the layout by applying an offset that either expands orshrinks the entire polygon. For example, the edges of the polysilicongates need to be offset by expanding each polygon in that layout layerto account for the sidewall spacers that surround each polysilicon gate.The stress contribution (positive or negative) caused by each edgeconsidered within the loop of step 512 will be taken into account in thedetermination of the total stress at the current sample point.

In step 512, another loop is begun, nested within the loop of step 510,through the three dimensions of the layout. The third dimension (Z) maybe omitted in some embodiments. All the edges shown in FIG. 1 willintroduce stress in all three directions.

In step 514, the system approximates the contribution of the currentedge to the stress in the current direction at the current sample point.Reference is made to FIG. 6 in order to better explain this step. FIG. 6illustrates diffusion regions in a portion of the plan view of thelayout of FIG. 1. For STI-induced stress, the significant edges arethose bounding the diffusion regions. Edge 610 of diffusion region 130in FIG. 6 is the STI-boundary nearest sample point 310 toward the right,and continuing toward the right, edge 612 represents the end of the STIregion 134 in the rightward direction. Similarly, edge 630 of diffusionregion 130 in FIG. 6 is the STI-boundary nearest sample point 310 towardthe top of the drawing. Edge 610 is oriented in the Y direction and hasendpoints at (x₁, y₁) and (x₁, y₂). Edge 612 is also oriented in the Ydirection and has endpoints at (x₂, y₁) and (x₂, y₂). Edge 630 isoriented in the X direction and has endpoints at (x₃, y₁) and (x₁, y₁).The position of sample point 310 is referred to as (x₀, y₀).

Consider first the normal stress introduced in the X direction by theSTI edges oriented in the Y direction. Initially, the stress at samplepoint 310 due to a nearby edge 610 is considered. The stresscontribution in the X direction can be approximated by amaterials-dependent factor σ₀, times the decay function of the distancein the X direction between the current edge and the current samplepoint, times a decay function of the length in the Y direction of theedge. More specifically, the stress contribution σ_(xx) can beapproximated by:

σ_(xx)(x,y)=sign*σ₀*σ_(xx)(x)*σ_(xx)(y)  (1)

where

σ_(xx)(x)=λ_(x)(x ₀ −x ₁)  (2)

and

σ_(xx)(y)=λ_(y)(y ₀ −y ₂)−λ_(y)(y ₀ −y ₁)  (3)

and λ_(x)(r) and λ_(y)(r) are decay functions describing the reductionof the stress contribution as a function of distance in the X and Ydirections of the layout, respectively.

In eq. (1), the value of “sign” is +1 or −1, whichever is required suchthat near edges of an STI region (such as edge 610 in FIG. 6) produce apositive stress contribution σ_(xx) and far edges of an STI region (suchas edge 612 in FIG. 6 produce a negative stress contribution σ_(xx);because near edges of an STI region contribute additional stress whereasfar edges mitigate the stress contribution. It will be appreciated thatneither edge 612 nor the edge to the left of STI region 132 would havebeen taken into account in the prior art LOD method. Neither would theadditional Y-oriented edges disposed further to the right or left ofthese, or X-oriented edges such as edge 630 in FIG. 6.

The factor σ₀ is a function of the current stress generation mechanism.It can be calculated using a detailed TCAD finite element stressanalysis for example, or it can be extracted from electricalmeasurements of a specifically designed test structure. Once determined,σ₀ remains constant over the entire chip for a given manufacturingtechnology. Whenever the manufacturing process flow is modified, thestress distribution might be affected and therefore σ₀ has to bere-calibrated.

The decay function λ_(i)(r) can be different for different embodiments,and for different dimensions of the layout. Because of the difficulty ofderiving the true decay function from physical principles, mostembodiments will only approximate it. Roughly, the function chosenshould be strong but finite in the near field, asymptotically reducingto zero in the far field, and in the midfield it should behave somewherebetween the appropriate behavior for two extreme cases of approximationsof the actual geometry of the stress source: if the stress sourcerepresented by a layout edge were a line source on the surface of thechip, then the proper decay would have the form 1/r²; whereas if thestress source represented by a layout edge were a plane source extendingvertically into the chip, the plane containing the layout edge, then theproper decay would have the form 1/r. In fact the stress sourcerepresented by a layout edge is somewhere between those two extremes,which motivates a decay function of the form 1/r^(β), 1<β<2. In apreferred embodiment the following decay function is used for each i'thdimension:

λ_(i)(r)=1/(α_(i) *+r ^(βi)+ε_(i))  (4)

In eq. (4), β_(i) depends roughly on the depth into the chip of thestress source material, and can be on the order of 1.2 for both the Xand Y stress component directions. The factor α_(i) is determined bymechanical properties of silicon. The additive factor ε_(i) is small,much less than α_(i)*r^(βi). It is included in part to avoid thedegenerate result of infinite stress at r=0, and in part because it canimprove the accuracy of the midfield behavior of the function. Thevalues of α_(i), β_(i) and ε_(i), each of which may be different for thedifferent stress contribution directions X and Y, may be estimated usinga full TCAD simulation or calibrated using electrical measurements ofthe test structures.

Other types of decay function approximations can be used in otherembodiments. Another function type that might be used is the errorfunction, erfc(r). In some embodiments, the decay function λ_(i)(r)might not be strictly monotonic, especially in the very near field wherethe stress might increase slightly before beginning a monotonic decay.

For the normal stress component in the Y direction, similar equationscan be used. In the present embodiment, the stress contribution in the Ydirection due to edge 630, having endpoints (x3, y1) and (x1, y1) isapproximated by:

σ_(yy)(x,y)=sign*σ₀*σ_(yy)(x)*σ_(yy)(y)  (5)

where

σ_(yy)(x)=λ_(x)(x ₀ −x ₃)−λ_(x)(x ₀ −x ₁)  (6)

σ_(yy)(y)=λ_(y)(y ₀ −y ₁)  (7)

and λ_(i)(r) is as given in eq. (4).

Similarly, for the Z direction, again similar equations can be used.

Note that whereas the layout diagrams of FIGS. 1, 3 and 6 all illustratestructures whose edges are in either the X or Y directions of thelayout, it will be appreciated that the above formulas and the routineof FIG. 5 can be easily adapted for structures having edges that areoriented arbitrarily in the X-Y layout plane.

After the stress contribution due to the current edge in the currentdirection is approximated from eq. (1), it is added to a total stressvalue in the current direction at the current sample point (step 516).The routine then loops back to evaluating the stress contribution of thecurrent edge in the next layout dimension (step 518). If there are nomore dimensions to consider, then in step 520, the routine loops back tobegin considering the next diffusion-STI interface edge within thesearch region.

Returning to FIG. 4, in step 416, after the approximate contributions tothe stress at the current sample point of all stress generationmechanisms in the current search region have been added up, the routineloops back to step 410 to consider the stress contributions due to thenext stress generation mechanism. If there are no further stressgeneration mechanisms to consider, then in step 418, the routine loopsback to step 408 to approximate the stress at the next sample point. Ifthere are no more sample points to consider, then in step 420 theroutine terminates with an approximation of the total stress at eachsample point.

Returning now to FIG. 2, after the total stress has been approximated ateach sample point, the routine approximates the stress-induced mobilityenhancement due to such total stress at each sample point (step 218).This conversion from stress to mobility enhancement is well known, andcan be in the form:

Δμ=f _(x)(σ_(xx))+f _(y)(σ_(yy))+f _(z)(σ_(zz))  (8)

To a first order approximation, where the silicon wafer on which thelayout will be fabricated has (100) surface orientation and thetransistor channels are aligned with the <110> crystalline direction,the following functions can be used:

f _(x)(σ_(xx))=a*σ _(xx),

f _(y)(σ_(yy))=b*σ _(yy), and

f _(z)(σ_(zz))=c*σ _(zz)

where a=0.3, b=−0.5 and c=0.2 for electron mobility, andwhere a=−0.7, b=0 and c=0.7 for hole mobility. Different functions wouldbe used for different crystalline orientations of the wafer and thechannel.

In step 220, the mobility enhancements approximated for the severalsample points in the channel are averaged, to approximate the averagemobility enhancement for the entire channel in current transistor. Theactual mobility in the channel of the current transistor can then beapproximated as

μ=μ0+Δμ  (9)

where μ0 is the mobility in the channel before stress effects are takeninto account.

In step 222, if there are more transistors to be analyzed, the routinereturns to step 210 to determine the average mobility enhancement forthe next transistor. If not, then in step 224, modified mobility valuesfor the analyzed transistors can now be provided for circuit simulationor other purposes.

As used herein, a given value is “responsive” to a predecessor value ifthe predecessor value influenced the given value. If there is anintervening processing element or step, the given value can still be“responsive” to the predecessor value. If the intervening processingelement or step combines more than one value, the value output of theprocessing element or step is considered “responsive” to each of thevalue inputs. If the given value is the same as the predecessor value,this is merely a degenerate case in which the given value is stillconsidered to be “responsive” to the predecessor value. “Dependency” ofa given value upon another value is defined similarly.

The foregoing description of preferred embodiments of the presentinvention has been provided for the purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed. Obviously, many modificationsand variations will be apparent to practitioners skilled in this art.For example, whereas the description above focuses on modeling stressesand converting stresses into stress-induced mobility enhancements,stress also affects several other transistor properties. It is known toaffect the band gap structure and as a result of the modified band gapstructure it shifts the threshold voltage of the transistor understress. Stress that is applied early in the process flow can also affectthe dopant diffusion, activation, and segregation in the transistorchannel and source/drain and result in modified doping profiles in thechannel and source/drain. These other stress-induced modifications oftransistor properties are typically much weaker than the stress-inducedmobility enhancements, but nevertheless can be noticeable. Theapproaches described herein can be used for estimating such second-ordereffects in a similar way they are used to model stress-induced mobilityenhancements.

The embodiments were chosen and described in order to best explain theprinciples of the invention and its practical application, therebyenabling others skilled in the art to understand the invention forvarious embodiments and with various modifications as are suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the following claims and their equivalents.

1. A method for approximating stress-induced mobility variation in anintegrated circuit layout during the development of an integratedcircuit, the integrated circuit layout defining a plurality oftransistors each having a respective channel, comprising: approximatingthe stress at each of a plurality of sites in the channels of each ofmore than twelve of the transistors in the integrated circuit layout;converting the stress approximation at each of the sites to a respectivemobility variation value; combining the respective mobility variationvalue at all the sites in the channel of each particular one of the morethan twelve transistors, to develop an overall mobility variation valuefor that particular transistor; and providing for circuit simulation avalue dependent upon the mobility variation value developed for each ofthe more than twelve transistors.
 2. The method of claim 1, wherein themore than twelve transistors are distributed among more than threedistinct diffusion regions in the integrated circuit layout.
 3. Themethod of claim 1, wherein the integrated circuit layout defines alayout for a full integrated circuit chip, and wherein approximating thestress at each of a plurality of sites in the channel of each of morethan twelve transistors in the layout comprises approximating the stressat each of a plurality of sites in the channels of all transistors inthe layout.
 4. The method of claim 1, wherein converting the stressapproximations at each of the sites to a respective mobility variationvalue comprises, for each subject one of the sites in the channel of theparticular transistor: converting the approximated stress at the subjectsite in each of at least two dimensions to a respective mobilityvariation value for the respective dimension at the subject site; andcombining the mobility variation values for all the dimensions at thesubject site to develop the mobility variation value for the subjectsite.
 5. The method of claim 4, wherein converting the approximatedstress at the subject site in each of at least two dimensions to arespective mobility variation value for that dimension at the subjectsite comprises: evaluating a first conversion function of theapproximated stress in a first one of the dimensions at the subjectsite; and evaluating a second conversion function of the approximatedstress in a second one of the dimensions at the subject site, whereinthe first and second conversion functions are different.
 6. The methodof claim 1, wherein approximating the stress at each of a plurality ofsites comprises, for each given one of a plurality of dimensions and foreach subject one of the sites in the channel of the particulartransistor: for each particular one of a plurality of edges within asearch region for the given site, approximating a first stresscontribution due to the particular edge to the stress in the givendimension at the subject site; and combining the contributions to thestress in the given dimension at the subject site approximated due toall the edges in the plurality of edges, to develop a combined stress inthe given dimension at the subject site.
 7. The method of claim 6,wherein approximating a first stress contribution due to the particularedge to the stress in the given dimension at the subject site,comprises: approximating the stress contributions due to a particularedge to the stress in the given dimension at the subject site due toeach of a plurality of stress generation mechanisms; and combining thestress contributions due to the particular edge to the stress in thegiven dimension at the subject site approximated due to all of thestress generation mechanisms, to develop a combined stress in the givendimension at the subject site due to the particular edge, and whereinconverting the stress approximation at each of the sites to a respectivemobility variation value comprises, for each subject one of the sites inthe channel of the particular transistor: converting the approximatedstress at the subject site in each of the dimensions to a respectivemobility variation value for that dimension at the subject site; andcombining the mobility variation values for all the dimensions at thesubject site to develop the mobility variation value for the subjectsite.
 8. The method of claim 1, wherein the plurality of sites in thechannel of a given one of the transistors in the integrated circuitlayout are all disposed in a line oriented transversely across thechannel of the given transistor.
 9. The method of claim 1, furthercomprising fabricating an integrated circuit device in dependence uponthe mobility variation values.
 10. A method for approximatingstress-induced modification of a transistor property in an integratedcircuit layout during the development of an integrated circuit, theintegrated circuit layout defining a plurality of transistors eachhaving a respective channel, comprising: approximating the stress ateach of a plurality of sites in the channels of each of more than twelveof the transistors in the integrated circuit layout; converting thestress approximation at each of the sites to a respective modificationvalue for the transistor property; combining the respective transistorproperty modification value at all the sites in the channels of eachparticular one of the more than twelve transistors, to develop anoverall transistor property modification value for that particulartransistor; and providing for circuit simulation a value dependent uponthe transistor property modification value developed for each of themore than twelve transistors.
 11. The method of claim 10, wherein thetransistor property is mobility.
 12. The method of claim 10, wherein thetransistor property is a transistor threshold voltage.
 13. The method ofclaim 10, wherein the transistor property is a doping profile in thechannel.
 14. The method of claim 10, wherein the plurality of sites inthe channel of a given one of the transistors in the integrated circuitlayout are all disposed in a line oriented transversely across thechannel of the given transistor.
 15. The method of claim 10, furthercomprising fabricating an integrated circuit device in dependence uponthe transistor property modification values.
 16. A method forapproximating stress-induced mobility variation in an integrated circuitlayout, the integrated circuit layout defining a plurality oftransistors each having a respective channel, comprising: approximatingthe stress at each of a plurality of sites in the channel of more thanthree transistors distributed among more than three distinct diffusionregions in the integrated circuit layout; converting the stressapproximation at each of the sites in the channels of each of the morethan three transistors to a respective mobility variation value;combining the respective mobility variation value at all the sites inthe channel regions of each particular one of the more than threetransistors, to develop an overall mobility variation value for thatparticular transistor; and providing for circuit simulation a valuedependent upon the mobility variation value developed for each of themore than three transistors.
 17. The method of claim 16, whereinconverting the stress approximations at each of the sites to arespective mobility variation value comprises, for each subject one ofthe sites in the channel of the particular transistor: converting theapproximated stress at the subject site in each of at least twodimensions to a respective mobility variation value for that dimensionat the subject site; and combining the mobility variation values for allthe dimensions at the subject site to develop the mobility variationvalue for the subject site.
 18. The method of claim 17, whereinconverting the approximated stress at the subject site in each of atleast two dimensions to a respective mobility variation value for thatdimension at the subject site comprises: evaluating a first conversionfunction of the approximated stress in a first one of the dimensions atthe subject site; and evaluating a second conversion function of theapproximated stress in a second one of the dimensions at the subjectsite, wherein the first conversion function and the second conversionfunction are different.
 19. The method of claim 16, whereinapproximating the stress at each of a plurality of sites comprises, foreach given one of a plurality of dimensions and for each subject one ofthe sites in the channel of the particular transistor: for eachparticular one of a plurality of edges within a search region for thegiven site, approximating a first stress contribution due to theparticular edge to the stress in the given dimension at the subjectsite; and combining contributions to the stress in the given dimensionat the subject site approximated due to all the edges in the pluralityof edges, to develop a combined stress in the given dimension at thesubject site.
 20. The method of claim 19, wherein approximating a firststress contribution due to the particular edge to the stress in thegiven dimension at the subject site, comprises: approximating the stresscontributions due to a particular edge to the stress in the givendimension at the subject site due to each of a plurality of stressgeneration mechanisms; and combining the stress contributions due to theparticular edge to the stress in the given dimension at the subject siteapproximated due to all of the stress generation mechanisms, to developa combined stress in the given dimension at the subject site due to theparticular edge, and wherein converting the stress approximation at eachof the sites to a respective mobility variation value comprises, foreach subject one of the sites in the channel of the particulartransistor: converting the approximated stress at the subject site ineach of the dimensions to a respective mobility variation value for thatdimension at the subject site; and combining the mobility variationvalues for all the dimensions at the subject site to develop themobility variation value for the subject site.
 21. The method of claim16, wherein the plurality of sites in the channel of a given one of thetransistors in the integrated circuit layout are all disposed in a lineoriented transversely across the channel of the given transistor. 22.The method of claim 16, further comprising fabricating an integratedcircuit device in dependence upon the mobility variation values.
 23. Amethod for approximating stress-induced modification of a transistorproperty in an integrated circuit layout, the integrated circuit layoutdefining a plurality of transistors each having a respective channel,comprising: approximating the stress at each of a plurality of sites inthe channels of more than three transistors distributed among more thanthree distinct diffusion regions in the integrated circuit layout;converting the stress approximation at each of the sites in the channelsof each of the more than three transistors to a respective transistorproperty modification value; combining the respective transistorproperty modification value at all the sites in the channels of eachparticular one of the more than three transistors, to develop an overalltransistor property modification value for that particular transistor;and providing for circuit simulation a value dependent upon thetransistor property modification value developed for each of more thanthree transistors.
 24. The method of claim 23, wherein transistorproperty is mobility.
 25. The method of claim 23, wherein the transistorproperty is a transistor threshold voltage.
 26. The method of claim 23,wherein the transistor property is a doping profile in the channel. 27.The method of claim 23, wherein the plurality of sites in the channel ofa given one of the transistors in the integrated circuit layout are alldisposed in a line oriented transversely across the channel of the giventransistor.
 28. The method of claim 23, further comprising fabricatingan integrated circuit device in dependence upon the transistor propertymodification values.
 29. A product for approximating stress-inducedmobility variation in an integrated circuit layout, the integratedcircuit layout defining a plurality of transistors each having arespective channel, comprising: means for approximating the stress ateach of a plurality of sites in the channels of each of more than twelveof the transistors in the integrated circuit layout; means forconverting the stress approximation at each of the sites to a respectivemobility variation value; and means for combining the respectivemobility variation value at all the sites in the channel of eachparticular one of the more than twelve transistors, to develop anoverall mobility variation value for that particular transistor.
 30. Theproduct of claim 29, wherein the means for converting the stressapproximations at each of the sites to a respective mobility variationvalue comprises means for, for each subject one of the sites in thechannel of the particular transistor, converting the approximated stressat the subject site in each of at least two dimensions to a respectivemobility variation value for the respective dimension at the subjectsite, and combining the mobility variation values for all the dimensionsat the subject site to develop the mobility variation value for thesubject site.
 31. The product of claim 29, wherein the means forapproximating the stress at each of a plurality of sites comprises meansfor, for each given one of a plurality of dimensions and for eachsubject one of the sites in the channel of the particular transistor:approximating, for each particular one of a plurality of edges within asearch region for the given site, a first stress contribution due to theparticular edge to the stress in the given dimension at the subjectsite; and combining the contributions to the stress in the givendimension at the subject site approximated due to all the edges in theplurality of edges, to develop a combined stress in the given dimensionat the subject site.
 32. A product for approximating stress-inducedmodification of a transistor property in an integrated circuit layout,the integrated circuit layout defining a plurality of transistors eachhaving a respective channel, comprising: means for approximating thestress at each of a plurality of sites in the channels of each of morethan twelve of the transistors in the integrated circuit layout; meansfor converting the stress approximation at each of the sites to arespective modification value for the transistor property; and means forcombining the respective transistor property modification value at allthe sites in the channels of each particular one of the more than twelvetransistors, to develop an overall transistor property modificationvalue for that particular transistor.
 33. The product of claim 32,wherein the transistor property is a transistor threshold voltage.
 34. Aproduct for approximating stress-induced mobility variation in anintegrated circuit layout, the integrated circuit layout defining aplurality of transistors each having a respective channel, comprising:means for approximating the stress at each of a plurality of sites inthe channel of more than three transistors distributed among more thanthree distinct diffusion regions in the integrated circuit layout; meansfor converting the stress approximation at each of the sites in thechannels of each of the more than three transistors to a respectivemobility variation value; and means for combining the respectivemobility variation value at all the sites in the channel regions of eachparticular one of the more than three transistors, to develop an overallmobility variation value for that particular transistor.
 35. A productfor approximating stress-induced modification of a transistor propertyin an integrated circuit layout, the integrated circuit layout defininga plurality of transistors each having a respective channel, comprising:means for approximating the stress at each of a plurality of sites inthe channels of more than three transistors distributed among more thanthree distinct diffusion regions in the integrated circuit layout; meansfor converting the stress approximation at each of the sites in thechannels of each of the more than three transistors to a respectivetransistor property modification value; and means for combining therespective transistor property modification value at all the sites inthe channels of each particular one of the more than three transistors,to develop an overall transistor property modification value for thatparticular transistor.